To measure the masses, radii, and densities of stars in a binary star
system

Grading Policy
There are two parts to this lab. The IUE data analysis must be done. The 14"
observations must be attempted, but things can go wrong. You need not do
the 14" observations if:

None of the eclipsing binaries will eclipse at night during your lab.
If there will be an eclipse the 4th week (but not earlier),
you can have an extra week to hand in your lab report.

The weather is bad. Keep a weather log. Eclipses may be clouded out.
If there are multiple eclipse opportunities, you must demonstrate that
you attempted an observation by the second week of the lab. We realize that
you have other work to do, so if you make at least 6 attempts to observe,
and all fail, then you need not try again. However, you must learn to use
the telescope/CCD (this can be done on a cloudy night).

The telescope, CCD, or acquisition computer fails. This is in the category
of bad weather. The TA or instructor must verify equipment failures.

If it appears that you will have difficulty completing the
optical observations, you must discuss the situation with the instructor as
soon as possible, and before the last week of the lab. We have
previously-obtained data which you can analyze.
The grade will be based on the quality of the data analysis and interpretation.
In the absence of extenuating circumstances, the archival data analysis, or the
optical data analysis, alone can be worth no more than a B grade.

Newtonian gravity is a powerful diagnostic tool. Given that gravity
is a 1/r2 central force, one can derive Kepler's Laws,
conservation of energy, and conservation of angular momentum. One can then
use these laws to determine the masses of stars. Mass is the fundamental
parameter which drives stellar evolution, unfortunately stellar masses can
only be determined when you have gravity - i.e., in a binary star
system.

To determine the stellar masses, you need to know the orbital period
P and the
semi-major axisa of the orbit. You can determine
a from P and the orbital velocity.

The point of this exercise is to apply Newton's laws and
Kepler's
laws.
You will verify the orbital period by obtaining
optical photometry using the 14" telescope. You will determine the
orbital velocity from archival IUE spectra. This will yield the masses.
In addition, you will use
the timing of the eclipse to determine the stellar radii.

You must take care of the following details during the first lab session:

Select a suitable target to observe. Read
section III.. You will need to know what targets
are observable at this time of year. Read the tutorials on
times and coordinate
systems.

Arrange with your TA to learn how to use the 14" telescope.

Examine the IUE database (Section V),
and ensure that there are LWP-HI or LWR-HI observations
you can use. If there are not enough (and this is the case for some good
optical targets), then you may do the IUE data analysis on another target.

Inform the instructor or the TA what your target(s) will be, and why you
chose it (them).

I searched for eclipsing binaries with periods longer than 8 hours
(to exclude contact binaries)
and less than 2 days (so there's an eclipse every day), with
the further constraints that the declination is greater than -10o
and the primary spectral type is F or later. I found
13 candidates in the CABS database, and
16 candidates in the Batten database (there is
overlap).
Select a star from one of these lists, or from someplace else if you have
another target.
Then

Look up the orbital elements,
and predict the times of eclipse.
Note that telescopic observations are best
done during nighttime hours. You
can find orbital elements in either the CABS or Batten databases.
Note that these orbital elements are old, and extrapolation to the present
epoch can lead to significant errors (if the uncertainty on a 1 day period
is +/- 1 minute (0.07% accuracy), and the last epoch of minimum was in
1980, the uncertainty on the extrapolated phase is now about 200%!).
Therefore ...

You must double-check the period and epoch using recent references.
You can find these in the ADS or
SIMBAD databases.
The IBVS
(Information Bulletin on Variable Stars) may have the most recent
lightcurves.

To download issues of the IBVS, do the following:

Find the issue you want to download at the IBVS web site.

Right-click on the *.ps.Z (compressed postscript)
file, and move the cursor to the
Save the Link As line to download the file.

Use WinZip to uncompress the
file. Make sure you are using the
"Classic Option", and not the "Wizard Option" in WinZip.

If you click on the file name, it should come up in a Ghostview
window. Alternatively, run Ghostview
and open the postscript file.

The IBVS is also
available in the Science and Engineering Library.

Go to the IUE catalog, and make sure there are LWP-HI or LWR-HI
exposures near the
times of quadratures.
If there are, request these data from NDADS. If not,
try another star.

Figure out how to find this star with the 14" telescope. Because the
telescope has no good setting circles, we use a star hopping technique.
First, find a nearby bright star. You can search the Yale Bright Star
Catalog, which is available as an on-line IDL database. You can use the
Digitized Sky Survey
(available on-line from the
HST/MAST archives) to
make a finding chart, if necessary. Note that the positions in the
Batten catalog are equinox 1900; IUE used equinox 1950, and the HST uses
equinox 2000 coordinates. You may have to precess your coordinates.

Because star hopping can be tedious, it may take up to an hour or two
to find the
star. It would be best if the eclipse occurred in the second half of the
night, at least until you are adept at finding the target.
WARNING: it may be very difficult to find your target when
the Moon is nearly full. If possible, try not to observe near the full
Moon.

To figure out whether your star is observable at this time of year, you need
to know the local sidereal time at midnight.
You can use the IDL procedure LMST (type
print,lmst(/help) for on-line help), or you can use
the SKYCAL utility (click on the SKYCAL icon
on the PC).

Sample images of stars that have already been observed as part of this lab
are:

Prior to using the telescope, you will be given a lesson by a TA or other
experienced observer. You may wish to assist others on a few observing
sessions prior to your first solo night. Note that no one is allowed to
observe alone: for safety reasons you must have an observing partner.

The telescope is heavily booked.
You must sign
up on the board outside room ESS 443C.

We will use IUE data because IUE offers a large and uniform spectroscopic
archive. The IUE obtained spectra in two wavelength ranges: 1150-1950
(short wavelength, or SW)
and 1900-3200 (long wavelength, or LW) Angstroms. It offered both low
(6 Angstroms resolution) and high (10,000 resolution) dispersion. The
high dispersion used an echelle spectrograph,
which permited the full spectral range to be imaged simultaneously on a
2-dimensional detector.
In particular, observations with the LWP or LWR (the P and R
refer to the prime and redundant cameras) cameras in high dispersion
reveal the Mg II h and k lines in emission in chromospherically-active
stars. By measuring the radial velocities of the Mg II lines at opposite
quadratures, you can determine the orbital velocities of the stars.
You will search the archive for appropriate observations of your targets.

You will downoad the IUE data from the
MAST archives.
Instructions for searching MAST are
here.
Use the IUE Search Form.

Enter your target name (e.g., ER Vul)

set the Camera to LWP and LWR (uncheck SWP)

set the Dispersion to High

set the Aperture to Large

Then click on the "Search" button. When the search results come up,
mark the images you want (probably all of them), and click the
"Download NEWSIPS MX files as a .tar file" button. A filke called
iue.tar should be directly downloaded to you.
Extract the files using wtar; then will be written to a subdirectory called
"iue". These file have ".mxhi" extensions, but they are
Fits format.

You want to identify a stellar line (preferably one in each star), and measure
its wavelength as a function of time. Use the Doppler effect to determine the
radial velocity as a function of orbital phase, and determine the maximum
velocity for each star. You will also need to determine the systemic, or
,
velocity for the
star. You can determine this directly by observing at phase 0 and 180.

This must be done using high dispersion spectra. The best line to use is the
2795/2802 Angstrom Mg II doublet
(the resonance lines of singly ionized
Magnesium). Mg II is in emission in all rapidly rotating late-type stars.
The rest wavelengths of the line are 2795.523 and 2802.698 Angstroms.
Note that these are air wavelengths. By convention, wavelengths greater than
2000 Angstroms are generally quoted in air, while wavelengths shorter than
2000 Angstroms are quoted in vacuum. When the IUE project reprocessed their
data, they chose to use the vacuum wavelength scale for all their data.
The ratio of the vacuum
to air wavelengths is the index of
refraction of air.

The Optical Data

You want to measure the flux
of the star as a function of time through its
eclipse. It is almost impossible to make an absolute flux measurement from
Stony Brook, so we rely on differential photometry. Choose another star in the
CCD field, and measure its brightness too. The other star is most likely not
as variable as the eclipsing binary (Most stars are binaries, however, so you
might check this one out just in case. Try the General Catalog of Variable
Stars.).

If you are unable to do the observations because of inclement weather
(or any other reason), you must still undertake the imaging analysis.
There is a sequence of images of RT And available in the directory
\phy515\rtand. Analyze these as though you took them. The
readme.txt file describes the files; you will need to read the
headers to learn the exposure times and times of observation.

0.4 times the logarithm of the ratio of counts is the
magnitude difference.
If there is no other star in the CCD image, or if the star is very faint (hence
noisy), find a nearby star about as bright as the eclipsing binary, and observe
it frequently to monitor trends in transparency.

Of course, photometry is not really this easy. Details can be found
here.

Plot the brightness of the target as a function of time. If you did
everything right, you should see a decrease in brightness followed by a
return to the original brightness centered on the time of eclipse.

In order to do these reductions, you will have to learn how to display and
analyze your images using IDL. Before you take your own data, you may practice
reducing images and preparing your software using the files
c:\idl\testdata\test.fit (an image of RT And) and
c:\idl\testdata\test_flat.fit
(a flat field image).

The basic data reduction involved extracting the subarray of data containing
the star (star=image(x1:x2,y1:y2)) and a subarray
containing the background. Use the total command to determine the
number of counts. Scale the background counts to the area of the star
subarray, and subtract the background. Do the same for the comparison star, and
record the ratio of counts. If you have many images, consider writing a
program to loop through the images, doing this automatically.

When determining the eclipse times, or the
times of contact,
it is sufficient to model the eclipse
as four straight line segments (see figure).
Assume the brightness is constant outside eclipse. Further assume,
if the eclipse is total or annular, constant brightness between
2nd and 3rd contacts. Assume that the light curve
between 1st and 2nd contacts, and between 3rd
and 4th, can be modeled as a linear function of time. The
intersections of these 4 line segments provide a good estimate of the times
of contact.

Why do we use differential photometry? What conditions do you need
for absolute photometry?

How do you use the orbital velocities and the length of the eclipse to
determine the radii of the two stars?

At primary minimum, which star is in front and which is behind? Answer this
for your binary, not in general. What can you say about the relative
temperatures of the two stars?

What is the narrow absorption line in the IUE Mg II spectra, and why doesn't
its wavelength change?

What are your best estimates of the masses and radii of the stars? Include
error estimates. Look up the true masses and radii in the CABS, and comment
on the differences between your estimates and the truth, especially if
your error bars are too small.